| For practicing researchers and statisticians who need to update their knowledge, this is the first book devoted to the negative binomial model and its many variations. Covers every model currently offered in commercial statistical software packages in detail, with numerous examples of their application and specific guidance on modeling strategy. |
| Joseph M. Hilbe is Emeritus Professor of Philosophy, University of Hawaii, and Adjunct Professor of Statistics, Arizona State University; Fellow, American Statistical Association; Fellow, Royal Statistical Society; Software Reviews Editor, The American Statistician (since 1997). His books include Negative Binomial Regression (2007, Cambridge University Press), Generalized Estimating Equations (with J. Hardin; 2002, CRC Press), and Generalized Linear Models and Extensions (with J. Hardin; 2001, 2007, Stata Press). |
| Preface Introduction 1 Overview of count response models 1.1 Varieties of count response model 1.2 Estimation 1.3 Fit considerations 1.4 Brief history of the negative binomial 1.5 Summary 2 Methods of estimation 2.1 Derivation of the IRLS algorithm 2.2 Newton–Raphson algorithms 2.3 The exponential family 2.4 Residuals for count response models 2.5 Summary 3 Poisson regression 3.1 Derivation of the Poisson model 3.2 Parameterization as a rate model 3.3 Testing overdispersion 3.4 Summary 4 Overdispersion 4.1 What is overdispersion? 4.2 Handling apparent overdispersion 4.3 Methods of handling real overdispersion 4.4 Summary 5 Negative binomial regression 5.1 Varieties of negative binomial 5.2 Derivation of the negative binomial 5.3 Negative binomial distributions 5.4 Algorithms 5.5 Summary 6 Negative binomial regression: modeling 6.1 Poisson versus negative binomial 6.2 Binomial versus count models 6.3 Examples: negative binomial regression 6.4 Summary 7 Alternative variance parameterizations 7.1 Geometric regression 7.2 NB-1: The linear constant model 7.3 NB-H: Heterogeneous negative binomial regression 7.4 The NB-P model 7.5 Generalized Poisson regression 7.6 Summary 8 Problems with zero counts 8.1 Zero-truncated negative binomial 8.2 Negative binomial with endogenous stratification 8.3 Hurdle models 8.4 Zero-inflated count models 8.5 Summary 9 Negative binomial with censoring, truncation, and sample selection 9.1 Censored and truncated models – econometric parameterization 9.2 Censored poisson and NB-2 models – survival parameterization 9.3 Sample selection models 9.4 Summary 10 Negative binomial panel models 10.1 Unconditional fixed-effects negative binomial model 10.2 Conditional fixed-effects negative binomial model 10.3 Random-effects negative binomial 10.4 Generalized estimating equation 10.5 Multilevel negative binomial models 10.6 Summary Appendix A: Negative binomial log-likelihood functions Appendix B: Deviance functions Appendix C: Stata negative binomial – ML algorithm Appendix D: Negative binomial variance functions Appendix E: Data sets References Author index Subject index |
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